> ## Documentation Index
> Fetch the complete documentation index at: https://docs.vibetoken.cn/llms.txt
> Use this file to discover all available pages before exploring further.

# Vibe Token Formula Reference: All Six Economic Equations

> Complete reference for all six Vibe Token formulas: pricing, earning, distribution, exit value, exit queue, and the pricing constant.

Every economic behavior in Vibe Token — how price moves, how tokens are earned, how distributions flow, and how exits are valued — is governed by six formulas. This page defines each one, explains its variables, and walks through a concrete example so you know exactly how the math works.

***

## 1. Token Price

<CodeGroup>
  ```text Formula theme={null}
  P = k × √S
  ```
</CodeGroup>

**Variables**

| Variable | Meaning                                 |
| -------- | --------------------------------------- |
| `P`      | Token price (in dollars)                |
| `k`      | Pricing constant                        |
| `S`      | Circulating supply (issued tokens only) |

Price is a direct function of supply. Every token minted raises the price slightly; every token burned lowers it. There are no external market forces, no order books, and no speculation — the price is always computable from first principles.

**Worked example**

> `k = 0.01`, `S = 10,000`
>
> `P = 0.01 × √10,000 = 0.01 × 100 = $1.00`

***

## 2. Pricing Constant

<CodeGroup>
  ```text Formula theme={null}
  k = max(MRR ÷ 1,000,000, 0.005)
  ```
</CodeGroup>

**Variables**

| Variable | Meaning                                |
| -------- | -------------------------------------- |
| `MRR`    | Monthly recurring revenue (in dollars) |

`k` anchors token price to your business's revenue scale. Dividing MRR by 1,000,000 keeps prices in a sensible dollar range across businesses of very different sizes. The floor of `0.005` ensures that even pre-revenue or very early-stage businesses have a nonzero starting price.

**Worked examples**

> **MRR = \$10,000**
>
> `k = max(10,000 ÷ 1,000,000, 0.005) = max(0.01, 0.005) = 0.01`

> **MRR = \$2,000**
>
> `k = max(2,000 ÷ 1,000,000, 0.005) = max(0.002, 0.005) = 0.005` (floor applies)

***

## 3. Token Earning

<CodeGroup>
  ```text Formula theme={null}
  tokens = floor(α × dR ÷ P)
  ```
</CodeGroup>

**Variables**

| Variable | Meaning                                      |
| -------- | -------------------------------------------- |
| `α`      | Revenue share (founder-specified, immutable) |
| `dR`     | New revenue event amount (in dollars)        |
| `P`      | Current token price at the time of the event |

When a revenue event occurs, the contributor's share of that revenue (`α × dR`) is converted into whole tokens at the current price. The `floor()` function ensures tokens are always whole integers — no fractional tokens are ever issued.

**Worked example**

> `α = 0.20`, `dR = $500`, `P = $1.00`
>
> `tokens = floor(0.20 × 500 ÷ 1.00) = floor(100) = 100 tokens`

***

## 4. Revenue Distribution

<CodeGroup>
  ```text Formula theme={null}
  D = α × dR
  payout per token = D ÷ S
  ```
</CodeGroup>

**Variables**

| Variable | Meaning                                        |
| -------- | ---------------------------------------------- |
| `D`      | Distribution pool for this revenue event       |
| `α`      | Revenue share                                  |
| `dR`     | New revenue event amount (in dollars)          |
| `S`      | Circulating supply at the time of distribution |

Every revenue event splits into two effects: tokens are minted for the contributor (see Token Earning above), and the same revenue share funds a cash distribution to all existing holders. Your payout is proportional to the fraction of supply you hold.

**Worked example**

> `α = 0.20`, `dR = $1,000`
>
> `D = 0.20 × $1,000 = $200`
>
> `S = 5,000` → `payout per token = $200 ÷ 5,000 = $0.04`

***

## 5. Exit Value

<CodeGroup>
  ```text Formula theme={null}
  exit_value = tokens × P
  ```
</CodeGroup>

**Variables**

| Variable | Meaning                                       |
| -------- | --------------------------------------------- |
| `tokens` | Number of tokens you are burning in this exit |
| `P`      | Token price at the time of the exit           |

When you exit, your tokens are burned and you receive their current market value. Because `P` is supply-based, the price at exit depends on how much the supply has grown or shrunk since you earned those tokens. Exiting also reduces `S`, which lowers `P` slightly for remaining exits.

**Worked example**

> `tokens = 300`, `P = $2.50`
>
> `exit_value = 300 × $2.50 = $750`

***

## 6. Supply Floor

<CodeGroup>
  ```text Formula theme={null}
  Smin = 1,000
  ```
</CodeGroup>

`Smin` is the minimum circulating supply. It exists to prevent the price formula `P = k × √S` from approaching zero as supply shrinks — a mathematical singularity that would make the system unworkable. Supply is never allowed to fall below 1,000, even if burns would otherwise push it lower.

**Worked example**

> At `Smin` with `k = 0.005`:
>
> `P = 0.005 × √1,000 = 0.005 × 31.62 ≈ $0.158`

This means even in the worst case — minimal supply and the floor pricing constant — there is always a nonzero, meaningful token price.

***

## Variable Glossary

| Variable | Meaning                                      |
| -------- | -------------------------------------------- |
| `P`      | Token price                                  |
| `k`      | Pricing constant                             |
| `S`      | Circulating supply (issued only)             |
| `Smin`   | Minimum supply floor (1,000)                 |
| `α`      | Revenue share (founder-specified, immutable) |
| `dR`     | New revenue event amount                     |
| `R`      | Cumulative lifetime revenue                  |
| `D`      | Distribution pool per revenue event          |